In the meta-learning setup, inspired by the PAC-Bayes bounds for conventional learning problem, by using different convex functions, different kinds of bounds were obtained [1]}, [2]}, [3]}, [4]}, [5]}.
Initially, an extension of generalization error bounds to meta-learning was provided in [1]} with a convergence rate \(O(1/\sqrt{{}})+O(1/(\sqrt{{\mathrm {M}}})+1/\sqrt{\mathrm {M}})\) . To have tighter bounds, the approaches proposed in [7]} and [8]} have been extended to the meta-learning problem in [2]} and [3]}, respectively.
In [2]} with a rate \(O(\sqrt{\log ()/{}})+O(\sqrt{\log (\mathrm {M})/{\mathrm {M}}}\) , by minimizing the obtained PAC-Bayes bound, a gradient-based algorithm was proposed. In [3]} with a convergence rate \(O(1/\sqrt{{}})+O(1/(\sqrt{{\mathrm {M}}})+1/\sqrt{})\) , by optimizing the obtained bound, a class of PAC-optimal meta-learning algorithms was developed. To achieve meta-learning algorithms with rapid convergence ability, [4]} and [5]} have studied fast-rate bounds for the meta-learning setup with improved complexities.
